Label Class Class size Class degree Base field Field degree Field signature Conductor Conductor norm Discriminant norm Root analytic conductor Bad primes Rank Torsion CM CM Sato-Tate $\Q$-curve Base change Semistable Potentially good Nonmax $\ell$ mod-$\ell$ images $Ш_{\textrm{an}}$ Tamagawa Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
22500.3-c2 22500.3-c $2$
$3$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
22500.3
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \)
\( 2^{4} \cdot 3^{6} \cdot 5^{4} \)
$2.18884$
$(a+1), (-a-2), (2a+1), (3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B $1$
\( 3 \)
$0.159999281$
$3.601411123$
3.457339142
\( -\frac{40960}{27} \)
\( \bigl[0\) , \( -i\) , \( i + 1\) , \( 3\) , \( -5 i\bigr] \) ${y}^2+\left(i+1\right){y}={x}^{3}-i{x}^{2}+3{x}-5i$
22500.3-f2 22500.3-f $2$
$3$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
22500.3
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \)
\( 2^{4} \cdot 3^{6} \cdot 5^{16} \)
$2.18884$
$(a+1), (-a-2), (2a+1), (3)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B.1.1 $1$
\( 3^{4} \)
$0.286792415$
$0.720282224$
3.718286617
\( -\frac{40960}{27} \)
\( \bigl[0\) , \( -i\) , \( i + 1\) , \( 83\) , \( 400 i\bigr] \) ${y}^2+\left(i+1\right){y}={x}^{3}-i{x}^{2}+83{x}+400i$
90000.3-c2 90000.3-c $2$
$3$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
90000.3
\( 2^{4} \cdot 3^{2} \cdot 5^{4} \)
\( 2^{4} \cdot 3^{6} \cdot 5^{10} \)
$3.09549$
$(a+1), (-a-2), (2a+1), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B $1$
\( 1 \)
$1$
$1.610600017$
1.610600017
\( -\frac{40960}{27} \)
\( \bigl[0\) , \( -i - 1\) , \( i + 1\) , \( 14 i - 10\) , \( 36 i + 1\bigr] \) ${y}^2+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(14i-10\right){x}+36i+1$
90000.3-r2 90000.3-r $2$
$3$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
90000.3
\( 2^{4} \cdot 3^{2} \cdot 5^{4} \)
\( 2^{4} \cdot 3^{6} \cdot 5^{10} \)
$3.09549$
$(a+1), (-a-2), (2a+1), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B $1$
\( 1 \)
$1$
$1.610600017$
1.610600017
\( -\frac{40960}{27} \)
\( \bigl[0\) , \( i - 1\) , \( i + 1\) , \( -14 i - 10\) , \( -37 i + 1\bigr] \) ${y}^2+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-14i-10\right){x}-37i+1$
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Pari/GP
SageMath
Magma
Oscar
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*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
